Would you like to re-read your question and check if it actually says what you mean to ask? Do you think it makes sense?

If you have saved the profile you could install it into a new installation of Thunderbird.

Yes, my question makes sense to me. I have dyslexia, dysgraphia and a language disorder. Perhaps you could specify what is not clear?

I have two computers. An iMac that I want to give away and a Macbook. I am giving away the iMac that has the emails that I need. My Macbook already has Thunderbird installed. I can't do a new installation, because I would lose the emails from the current installation.

You move the profile folder from one device to the other.

http://kb.mozillazine.org/Moving_your_profile_folder_-_Thunderbird

Then you install this add-on https://addons.mozilla.org/en-US/thunderbird/addon/profileswitcher/ into each profile so you have a menu entry to switch from profile to profile.

Finally, once you have the copy in place you tell the profile switcher to start with the profile manager and point to the folder containing your copied profile as a new profile. so the profile manager knows you have two profiles to switch between.